Statistical Inference

This course lays the foundation of Statistical Inference. The students would be taught the problems related to point and confidence interval estimation and testing of hypothesis. They would also be given the concepts of nonparametric and sequential test procedures and elements of decision theory.

 

  • Point estimation. Properties of estimators: Unbiasedness, Consistency, Efficiency and sufficiency. Frechet-Cramer-Rao inequality, Rao-Blackwell theorem, Completeness and bounded completeness, Basu’s theorem.
  • Methods of estimation: Maximum likelihood, Least squares, Minimum χ2,  Minimum distance, Moments, Maximum entropy.
  • Testing of hypothesis: randomized and non randomized tests, Neyman-Pearson lemma, Power function, Uniformly most powerful tests and their constructions, Unbiased tests, Likelihood ratio tests. Confidence-interval estimation.
  • Sequential analysis, Sequential probability ratio test. Elements of Decision theory and Bayesian inference.
  • Nonparametric tests: Run, Sign, Rank, Median, Wilcoxon-Mann-Whitney, Kruskal-Wallis, Friedmann two - way ANOVA by ranks.

 

Methods of estimation - Maximum Likelihood, Minimum c2 and Moments: Confidence Interval Estimation, MP and UMP tests, Large Sample tests, Non-parametric tests, Sequential Probability Ratio Test, Decision functions.